Conditional probability

Mathew has six cards.

He chooses three of the cards at random.

He does not replace any of the cards.

Calculate the probability that the first card is a 7, the second card is a 5 and the third

card is a 6.

Calculate the probability that the product of the numbers on Mathew’s three cards is a

cube number.

A bag contains 3 red counters, 5 blue counters and 7 yellow counters.

Sali takes three counters at random from the bag. These counters are not replaced.

Calculate the probability that at least two of the counters are the same colour.

Eleven cards are placed in a box.

Seven of the cards are red and the rest are blue.

Gareth selects two cards at random and does not replace them.

He claims that the probability of selecting two cards of the same colour is equal to the probability of selecting two cards of different colours.

Is Gareth correct?

You must show your working and justify your answer.

A box contains 5 blue discs and 3 yellow discs. Three discs are to be chosen at random, without replacement.

Calculate the probability that the three discs chosen will all be the same colour.

Calculate the probability that exactly one blue disc is selected.

Ffion has some blue cards and some yellow cards. She takes 7 of the blue cards and 3 of the yellow cards and puts them in a box.

Ffion removes one card from the box at random and replaces it with two cards of the other colour.

Then she removes a second card from the box at random.

Calculate the probability that the two cards that Ffion removed are of different colours.

The following nine cards are placed in a box.

Catherine chooses three cards at random from the box, without replacement.

Calculate the probability that the three cards drawn show the letters ‘A’, ‘F’ and ‘O’ in

that order.

Calculate the probability that two of the three cards show the same letter.

A bag contains 10 balls. 5 of the balls are blue, 4 of the balls are red and 1 ball is green. Three balls are chosen at random, one at a time, without replacement.

Calculate the probability that the first ball is blue, the second ball is red and the third ball is green.

You must show all your working.

Calculate the probability that at least one blue ball is chosen.

You must show all your working.

Three of the seven cards shown above are selected at random, without being replaced.

Find the probability that the first card selected is a 3, the second is a 4 and the third is

a 5.

Find the probability that the sum of the numbers selected is greater than 9.

Dewi has a box containing eleven socks.

Six of the socks are red, four are green and one is yellow.

Early one morning, without switching on the light, Dewi selects two socks at random.

Calculate the probability that the first sock selected is yellow and the second is red.

Calculate the probability that Dewi selects two socks of the same colour.

Calculate the probability that at least one green sock is selected.

Sixteen balls are placed in a bag.

Ten of the balls are green and six are yellow. Two balls are selected at random and not replaced.

Benjamin states that the probability of selecting two balls of the same colour is equal to the probability of selecting two balls of different colours.

Is Benjamin correct?

You must show all your working to justify your answer.

The following twelve cards are placed in a box.

Three cards are chosen at random from the box at the same time.

Calculate the probability that the three cards drawn are all the letter ‘C’.

The letters A, E and O are vowels. All the other letters on these cards are consonants.

Calculate the probability that the three cards drawn include at least one consonant and at

least one vowel.

A box contains 4 yellow cards and 6 red cards.

Three cards are chosen at random, one at a time, without replacement.

Calculate the probability that the first two cards are yellow and the third card is red.

You must show all your working.

Calculate the probability that at least one yellow card is chosen.

A raffle is held at a school fair and a total of 100 tickets are sold.

Angharad buys three of the tickets and Meirion buys one ticket. Tickets are selected at random and not replaced. The first prize to be awarded is a calculator. The second prize to be awarded is a voucher. No other prizes are awarded.

Calculate the probability that Angharad wins the calculator and Meirion wins the

voucher.

Calculate the probability that no one wins a prize apart from Angharad or Meirion.

A box contains 4 red balls, 5 yellow balls and 1 green ball.

Two balls are to be chosen at random, without replacement.

Find the probability of choosing 1 red ball and 1 green ball.

Find the probability that the two balls chosen will not be the same colour.

At a children’s party, the children play a number of games.

The winner of each game chooses a ticket for a prize, at random, from a box. The ticket is not returned to the box. At the start of the party, there are 12 prizes available: 1 book, 3 key-rings and 8 pencils.

Find the probability that the winners of the first two games choose the same type of

prize.

After the winners of the first three games have chosen their prizes, find the probability

that the ticket for the book is still in the box.

Two of the cards shown above are selected at random, without being replaced.

Find the probability that

the product of the two numbers selected is 12,

the sum of the two numbers selected is even.

A bag contains 5 red counters and 5 blue counters.

Three counters are drawn at random from the bag at the same time.

Calculate the probability that the three counters will be the same colour.

A bag contains 6 red blocks, 4 green blocks and 2 yellow blocks.

Three blocks are taken from the bag, at random, without replacement.

What is the probability that the first block removed is red, the second is green and the

third is yellow?

Calculate the probability that all three blocks will be the same colour.

Write down the probability that the three blocks will not be the same colour.